TSTP Solution File: SYN078+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN078+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 : n026.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 03:26:30 EDT 2023
% Result : Theorem 3.45s 1.26s
% Output : Proof 4.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN078+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 17:15:48 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.05/0.98 Prover 1: Preprocessing ...
% 2.05/0.98 Prover 4: Preprocessing ...
% 2.32/1.04 Prover 5: Preprocessing ...
% 2.32/1.04 Prover 3: Preprocessing ...
% 2.32/1.04 Prover 0: Preprocessing ...
% 2.32/1.04 Prover 6: Preprocessing ...
% 2.32/1.04 Prover 2: Preprocessing ...
% 2.98/1.14 Prover 2: Proving ...
% 2.98/1.14 Prover 6: Proving ...
% 2.98/1.15 Prover 5: Proving ...
% 2.98/1.15 Prover 4: Constructing countermodel ...
% 2.98/1.15 Prover 3: Constructing countermodel ...
% 2.98/1.16 Prover 0: Proving ...
% 2.98/1.16 Prover 1: Constructing countermodel ...
% 3.45/1.25 Prover 3: proved (591ms)
% 3.45/1.25
% 3.45/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.45/1.26
% 3.45/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.45/1.26 Prover 5: stopped
% 3.45/1.26 Prover 6: stopped
% 3.45/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.45/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.45/1.26 Prover 0: proved (608ms)
% 3.45/1.26 Prover 2: proved (602ms)
% 3.45/1.26
% 3.45/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.45/1.26
% 3.45/1.26
% 3.45/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.45/1.26
% 3.45/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.45/1.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.95/1.27 Prover 7: Preprocessing ...
% 3.95/1.27 Prover 8: Preprocessing ...
% 3.95/1.27 Prover 10: Preprocessing ...
% 3.96/1.27 Prover 11: Preprocessing ...
% 3.96/1.28 Prover 13: Preprocessing ...
% 3.96/1.29 Prover 7: Constructing countermodel ...
% 3.96/1.29 Prover 10: Constructing countermodel ...
% 3.96/1.30 Prover 8: Warning: ignoring some quantifiers
% 4.18/1.30 Prover 8: Constructing countermodel ...
% 4.18/1.31 Prover 13: Constructing countermodel ...
% 4.39/1.33 Prover 7: Found proof (size 9)
% 4.39/1.33 Prover 7: proved (72ms)
% 4.39/1.33 Prover 1: stopped
% 4.39/1.33 Prover 13: stopped
% 4.39/1.33 Prover 4: stopped
% 4.39/1.33 Prover 8: stopped
% 4.39/1.33 Prover 10: stopped
% 4.39/1.33 Prover 11: Constructing countermodel ...
% 4.39/1.33 Prover 11: stopped
% 4.39/1.33
% 4.39/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.39/1.33
% 4.39/1.34 % SZS output start Proof for theBenchmark
% 4.39/1.34 Assumptions after simplification:
% 4.39/1.34 ---------------------------------
% 4.39/1.34
% 4.39/1.34 (pel56)
% 4.39/1.38 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v3)
% 4.39/1.38 & $i(v1) & $i(v0) & ((v2 = v0 & f(v1) = v0 & big_p(v1) & ~ big_p(v0) & !
% 4.39/1.38 [v5: $i] : ! [v6: $i] : ( ~ (f(v5) = v6) | ~ $i(v5) | ~ big_p(v5) |
% 4.39/1.38 big_p(v6))) | (f(v3) = v4 & $i(v4) & big_p(v3) & ~ big_p(v4) & !
% 4.39/1.38 [v5: $i] : ! [v6: $i] : ( ~ (f(v6) = v5) | ~ $i(v6) | ~ $i(v5) | ~
% 4.39/1.38 big_p(v6) | big_p(v5)))))
% 4.39/1.38
% 4.39/1.38 Those formulas are unsatisfiable:
% 4.39/1.38 ---------------------------------
% 4.39/1.38
% 4.39/1.38 Begin of proof
% 4.39/1.38 |
% 4.39/1.38 | DELTA: instantiating (pel56) with fresh symbols all_3_0, all_3_1, all_3_2,
% 4.39/1.38 | all_3_3, all_3_4 gives:
% 4.39/1.39 | (1) $i(all_3_1) & $i(all_3_3) & $i(all_3_4) & ((all_3_2 = all_3_4 &
% 4.39/1.39 | f(all_3_3) = all_3_4 & big_p(all_3_3) & ~ big_p(all_3_4) & ! [v0:
% 4.39/1.39 | $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ big_p(v0) |
% 4.39/1.39 | big_p(v1))) | (f(all_3_1) = all_3_0 & $i(all_3_0) &
% 4.39/1.39 | big_p(all_3_1) & ~ big_p(all_3_0) & ! [v0: $i] : ! [v1: $i] : (
% 4.39/1.39 | ~ (f(v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ big_p(v1) |
% 4.39/1.39 | big_p(v0))))
% 4.39/1.39 |
% 4.39/1.39 | ALPHA: (1) implies:
% 4.39/1.39 | (2) $i(all_3_3)
% 4.39/1.39 | (3) $i(all_3_1)
% 4.39/1.40 | (4) (all_3_2 = all_3_4 & f(all_3_3) = all_3_4 & big_p(all_3_3) & ~
% 4.39/1.40 | big_p(all_3_4) & ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~
% 4.39/1.40 | $i(v0) | ~ big_p(v0) | big_p(v1))) | (f(all_3_1) = all_3_0 &
% 4.39/1.40 | $i(all_3_0) & big_p(all_3_1) & ~ big_p(all_3_0) & ! [v0: $i] : !
% 4.39/1.40 | [v1: $i] : ( ~ (f(v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ big_p(v1) |
% 4.39/1.40 | big_p(v0)))
% 4.39/1.40 |
% 4.39/1.40 | BETA: splitting (4) gives:
% 4.39/1.40 |
% 4.39/1.40 | Case 1:
% 4.39/1.40 | |
% 4.39/1.40 | | (5) all_3_2 = all_3_4 & f(all_3_3) = all_3_4 & big_p(all_3_3) & ~
% 4.39/1.40 | | big_p(all_3_4) & ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~
% 4.39/1.40 | | $i(v0) | ~ big_p(v0) | big_p(v1))
% 4.39/1.40 | |
% 4.39/1.40 | | ALPHA: (5) implies:
% 4.39/1.40 | | (6) ~ big_p(all_3_4)
% 4.39/1.40 | | (7) big_p(all_3_3)
% 4.39/1.40 | | (8) f(all_3_3) = all_3_4
% 4.39/1.40 | | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~
% 4.39/1.40 | | big_p(v0) | big_p(v1))
% 4.39/1.40 | |
% 4.39/1.41 | | GROUND_INST: instantiating (9) with all_3_3, all_3_4, simplifying with (2),
% 4.39/1.41 | | (6), (7), (8) gives:
% 4.39/1.41 | | (10) $false
% 4.39/1.41 | |
% 4.39/1.41 | | CLOSE: (10) is inconsistent.
% 4.39/1.41 | |
% 4.39/1.41 | Case 2:
% 4.39/1.41 | |
% 4.39/1.41 | | (11) f(all_3_1) = all_3_0 & $i(all_3_0) & big_p(all_3_1) & ~
% 4.39/1.41 | | big_p(all_3_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (f(v1) = v0) | ~
% 4.39/1.41 | | $i(v1) | ~ $i(v0) | ~ big_p(v1) | big_p(v0))
% 4.39/1.41 | |
% 4.39/1.41 | | ALPHA: (11) implies:
% 4.39/1.41 | | (12) ~ big_p(all_3_0)
% 4.39/1.41 | | (13) big_p(all_3_1)
% 4.39/1.41 | | (14) $i(all_3_0)
% 4.39/1.41 | | (15) f(all_3_1) = all_3_0
% 4.39/1.41 | | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v1) = v0) | ~ $i(v1) | ~ $i(v0)
% 4.39/1.41 | | | ~ big_p(v1) | big_p(v0))
% 4.39/1.41 | |
% 4.39/1.41 | | GROUND_INST: instantiating (16) with all_3_0, all_3_1, simplifying with (3),
% 4.39/1.41 | | (12), (13), (14), (15) gives:
% 4.39/1.41 | | (17) $false
% 4.39/1.41 | |
% 4.39/1.41 | | CLOSE: (17) is inconsistent.
% 4.39/1.41 | |
% 4.39/1.42 | End of split
% 4.39/1.42 |
% 4.39/1.42 End of proof
% 4.39/1.42 % SZS output end Proof for theBenchmark
% 4.39/1.42
% 4.39/1.42 779ms
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