TSTP Solution File: SYN059+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN059+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 : n009.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 03:26:23 EDT 2023
% Result : Theorem 3.83s 1.25s
% Output : Proof 4.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN059+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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 19:48:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.55/0.62 ________ _____
% 0.55/0.62 ___ __ \_________(_)________________________________
% 0.55/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.55/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.55/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.55/0.62
% 0.55/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.55/0.62 (2023-06-19)
% 0.55/0.62
% 0.55/0.62 (c) Philipp Rümmer, 2009-2023
% 0.55/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.55/0.62 Amanda Stjerna.
% 0.55/0.62 Free software under BSD-3-Clause.
% 0.55/0.62
% 0.55/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.55/0.62
% 0.55/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.63 Running up to 7 provers in parallel.
% 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.86/0.98 Prover 1: Preprocessing ...
% 1.86/0.99 Prover 4: Preprocessing ...
% 2.28/1.03 Prover 5: Preprocessing ...
% 2.28/1.03 Prover 6: Preprocessing ...
% 2.28/1.03 Prover 0: Preprocessing ...
% 2.28/1.03 Prover 2: Preprocessing ...
% 2.28/1.03 Prover 3: Preprocessing ...
% 2.61/1.11 Prover 2: Constructing countermodel ...
% 2.61/1.12 Prover 5: Constructing countermodel ...
% 3.16/1.16 Prover 3: Constructing countermodel ...
% 3.16/1.16 Prover 6: Proving ...
% 3.16/1.17 Prover 1: Constructing countermodel ...
% 3.38/1.18 Prover 4: Constructing countermodel ...
% 3.38/1.19 Prover 0: Proving ...
% 3.83/1.25 Prover 5: proved (610ms)
% 3.83/1.25
% 3.83/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.25
% 3.83/1.26 Prover 2: stopped
% 3.83/1.26 Prover 0: stopped
% 3.83/1.26 Prover 6: stopped
% 3.83/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.83/1.26 Prover 3: stopped
% 3.83/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.83/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.83/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.83/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.83/1.27 Prover 7: Preprocessing ...
% 3.83/1.27 Prover 11: Preprocessing ...
% 3.83/1.28 Prover 13: Preprocessing ...
% 3.83/1.28 Prover 8: Preprocessing ...
% 3.83/1.28 Prover 10: Preprocessing ...
% 3.83/1.30 Prover 13: Constructing countermodel ...
% 3.83/1.30 Prover 7: Constructing countermodel ...
% 3.83/1.31 Prover 10: Constructing countermodel ...
% 4.34/1.34 Prover 8: Warning: ignoring some quantifiers
% 4.34/1.34 Prover 8: Constructing countermodel ...
% 4.34/1.35 Prover 1: gave up
% 4.72/1.37 Prover 7: Found proof (size 23)
% 4.72/1.37 Prover 7: proved (104ms)
% 4.72/1.37 Prover 10: Found proof (size 23)
% 4.72/1.37 Prover 10: proved (99ms)
% 4.72/1.37 Prover 13: Found proof (size 23)
% 4.72/1.37 Prover 13: proved (98ms)
% 4.72/1.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.72/1.37 Prover 4: stopped
% 4.72/1.37 Prover 11: Constructing countermodel ...
% 4.72/1.37 Prover 8: stopped
% 4.72/1.37 Prover 11: stopped
% 4.72/1.38 Prover 16: Preprocessing ...
% 4.72/1.39 Prover 16: Constructing countermodel ...
% 4.72/1.39 Prover 16: stopped
% 4.72/1.39
% 4.72/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.72/1.39
% 4.72/1.40 % SZS output start Proof for theBenchmark
% 4.72/1.40 Assumptions after simplification:
% 4.72/1.40 ---------------------------------
% 4.72/1.40
% 4.72/1.40 (pel29)
% 4.72/1.41 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((big_g(v1) & big_f(v0) & !
% 4.72/1.41 [v2: $i] : ( ~ $i(v2) | ~ big_g(v2) | big_j(v2)) & ! [v2: $i] : ( ~
% 4.72/1.41 $i(v2) | ~ big_f(v2) | big_h(v2)) & ( ~ big_j(v1) | ~ big_h(v0))) |
% 4.72/1.41 ( ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ big_g(v3) | ~
% 4.72/1.41 big_f(v2) | big_j(v3)) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 4.72/1.41 $i(v2) | ~ big_g(v3) | ~ big_f(v2) | big_h(v2)) & ((big_g(v0) & ~
% 4.72/1.41 big_j(v0)) | (big_f(v0) & ~ big_h(v0))))))
% 4.72/1.41
% 4.72/1.41 (pel29_1)
% 4.72/1.41 ? [v0: $i] : ($i(v0) & big_f(v0))
% 4.72/1.41
% 4.72/1.41 (pel29_2)
% 4.72/1.41 ? [v0: $i] : ($i(v0) & big_g(v0))
% 4.72/1.41
% 4.72/1.41 Those formulas are unsatisfiable:
% 4.72/1.41 ---------------------------------
% 4.72/1.41
% 4.72/1.41 Begin of proof
% 4.72/1.41 |
% 4.72/1.41 | DELTA: instantiating (pel29_2) with fresh symbol all_2_0 gives:
% 4.72/1.41 | (1) $i(all_2_0) & big_g(all_2_0)
% 4.72/1.41 |
% 4.72/1.41 | ALPHA: (1) implies:
% 4.72/1.41 | (2) big_g(all_2_0)
% 4.72/1.41 | (3) $i(all_2_0)
% 4.72/1.41 |
% 4.72/1.41 | DELTA: instantiating (pel29_1) with fresh symbol all_4_0 gives:
% 4.72/1.41 | (4) $i(all_4_0) & big_f(all_4_0)
% 4.72/1.41 |
% 4.72/1.41 | ALPHA: (4) implies:
% 4.72/1.41 | (5) big_f(all_4_0)
% 4.72/1.41 | (6) $i(all_4_0)
% 4.72/1.41 |
% 4.72/1.41 | DELTA: instantiating (pel29) with fresh symbols all_6_0, all_6_1 gives:
% 4.72/1.42 | (7) $i(all_6_0) & $i(all_6_1) & ((big_g(all_6_0) & big_f(all_6_1) & ! [v0:
% 4.72/1.42 | $i] : ( ~ $i(v0) | ~ big_g(v0) | big_j(v0)) & ! [v0: $i] : ( ~
% 4.72/1.42 | $i(v0) | ~ big_f(v0) | big_h(v0)) & ( ~ big_j(all_6_0) | ~
% 4.72/1.42 | big_h(all_6_1))) | ( ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 4.72/1.42 | $i(v0) | ~ big_g(v1) | ~ big_f(v0) | big_j(v1)) & ! [v0: $i] :
% 4.72/1.42 | ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_g(v1) | ~ big_f(v0)
% 4.72/1.42 | | big_h(v0)) & ((big_g(all_6_1) & ~ big_j(all_6_1)) |
% 4.72/1.42 | (big_f(all_6_1) & ~ big_h(all_6_1)))))
% 4.72/1.42 |
% 4.72/1.42 | ALPHA: (7) implies:
% 4.72/1.42 | (8) $i(all_6_1)
% 4.72/1.42 | (9) $i(all_6_0)
% 4.72/1.42 | (10) (big_g(all_6_0) & big_f(all_6_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.72/1.42 | big_g(v0) | big_j(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ big_f(v0) |
% 4.72/1.42 | big_h(v0)) & ( ~ big_j(all_6_0) | ~ big_h(all_6_1))) | ( ! [v0:
% 4.72/1.42 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_g(v1) | ~
% 4.72/1.42 | big_f(v0) | big_j(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 4.72/1.42 | ~ $i(v0) | ~ big_g(v1) | ~ big_f(v0) | big_h(v0)) &
% 4.72/1.42 | ((big_g(all_6_1) & ~ big_j(all_6_1)) | (big_f(all_6_1) & ~
% 4.72/1.42 | big_h(all_6_1))))
% 4.72/1.42 |
% 4.72/1.42 | BETA: splitting (10) gives:
% 4.72/1.42 |
% 4.72/1.42 | Case 1:
% 4.72/1.42 | |
% 4.72/1.42 | | (11) big_g(all_6_0) & big_f(all_6_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 4.72/1.42 | | big_g(v0) | big_j(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ big_f(v0) |
% 4.72/1.42 | | big_h(v0)) & ( ~ big_j(all_6_0) | ~ big_h(all_6_1))
% 4.72/1.42 | |
% 4.72/1.42 | | ALPHA: (11) implies:
% 4.72/1.42 | | (12) big_f(all_6_1)
% 4.72/1.42 | | (13) big_g(all_6_0)
% 4.72/1.42 | | (14) ~ big_j(all_6_0) | ~ big_h(all_6_1)
% 4.72/1.42 | | (15) ! [v0: $i] : ( ~ $i(v0) | ~ big_f(v0) | big_h(v0))
% 4.72/1.42 | | (16) ! [v0: $i] : ( ~ $i(v0) | ~ big_g(v0) | big_j(v0))
% 4.72/1.42 | |
% 4.72/1.43 | | GROUND_INST: instantiating (15) with all_6_1, simplifying with (8), (12)
% 4.72/1.43 | | gives:
% 4.72/1.43 | | (17) big_h(all_6_1)
% 4.72/1.43 | |
% 4.72/1.43 | | GROUND_INST: instantiating (16) with all_6_0, simplifying with (9), (13)
% 4.72/1.43 | | gives:
% 4.72/1.43 | | (18) big_j(all_6_0)
% 4.72/1.43 | |
% 4.72/1.43 | | BETA: splitting (14) gives:
% 4.72/1.43 | |
% 4.72/1.43 | | Case 1:
% 4.72/1.43 | | |
% 4.72/1.43 | | | (19) ~ big_j(all_6_0)
% 4.72/1.43 | | |
% 4.72/1.43 | | | PRED_UNIFY: (18), (19) imply:
% 4.72/1.43 | | | (20) $false
% 4.72/1.43 | | |
% 4.72/1.43 | | | CLOSE: (20) is inconsistent.
% 4.72/1.43 | | |
% 4.72/1.43 | | Case 2:
% 4.72/1.43 | | |
% 4.72/1.43 | | | (21) ~ big_h(all_6_1)
% 4.72/1.43 | | |
% 4.72/1.43 | | | PRED_UNIFY: (17), (21) imply:
% 4.72/1.43 | | | (22) $false
% 4.72/1.43 | | |
% 4.72/1.43 | | | CLOSE: (22) is inconsistent.
% 4.72/1.43 | | |
% 4.72/1.43 | | End of split
% 4.72/1.43 | |
% 4.72/1.43 | Case 2:
% 4.72/1.43 | |
% 4.72/1.43 | | (23) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_g(v1) |
% 4.72/1.43 | | ~ big_f(v0) | big_j(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1)
% 4.72/1.43 | | | ~ $i(v0) | ~ big_g(v1) | ~ big_f(v0) | big_h(v0)) &
% 4.72/1.43 | | ((big_g(all_6_1) & ~ big_j(all_6_1)) | (big_f(all_6_1) & ~
% 4.72/1.43 | | big_h(all_6_1)))
% 4.72/1.43 | |
% 4.72/1.43 | | ALPHA: (23) implies:
% 4.72/1.43 | | (24) (big_g(all_6_1) & ~ big_j(all_6_1)) | (big_f(all_6_1) & ~
% 4.72/1.43 | | big_h(all_6_1))
% 4.72/1.43 | | (25) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_g(v1) |
% 4.72/1.43 | | ~ big_f(v0) | big_h(v0))
% 4.72/1.43 | | (26) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_g(v1) |
% 4.72/1.43 | | ~ big_f(v0) | big_j(v1))
% 4.72/1.43 | |
% 4.72/1.43 | | BETA: splitting (24) gives:
% 4.72/1.43 | |
% 4.72/1.43 | | Case 1:
% 4.72/1.43 | | |
% 4.72/1.43 | | | (27) big_g(all_6_1) & ~ big_j(all_6_1)
% 4.72/1.43 | | |
% 4.72/1.43 | | | ALPHA: (27) implies:
% 4.72/1.43 | | | (28) ~ big_j(all_6_1)
% 4.72/1.43 | | | (29) big_g(all_6_1)
% 4.72/1.43 | | |
% 4.72/1.43 | | | GROUND_INST: instantiating (26) with all_4_0, all_6_1, simplifying with
% 4.72/1.43 | | | (5), (6), (8), (28), (29) gives:
% 4.72/1.43 | | | (30) $false
% 4.72/1.43 | | |
% 4.72/1.43 | | | CLOSE: (30) is inconsistent.
% 4.72/1.43 | | |
% 4.72/1.43 | | Case 2:
% 4.72/1.43 | | |
% 4.72/1.43 | | | (31) big_f(all_6_1) & ~ big_h(all_6_1)
% 4.72/1.43 | | |
% 4.72/1.43 | | | ALPHA: (31) implies:
% 4.72/1.43 | | | (32) ~ big_h(all_6_1)
% 4.72/1.43 | | | (33) big_f(all_6_1)
% 4.72/1.43 | | |
% 4.72/1.43 | | | GROUND_INST: instantiating (25) with all_6_1, all_2_0, simplifying with
% 4.72/1.43 | | | (2), (3), (8), (32), (33) gives:
% 4.72/1.44 | | | (34) $false
% 4.72/1.44 | | |
% 4.72/1.44 | | | CLOSE: (34) is inconsistent.
% 4.72/1.44 | | |
% 4.72/1.44 | | End of split
% 4.72/1.44 | |
% 4.72/1.44 | End of split
% 4.72/1.44 |
% 4.72/1.44 End of proof
% 4.72/1.44 % SZS output end Proof for theBenchmark
% 4.72/1.44
% 4.72/1.44 818ms
%------------------------------------------------------------------------------