TSTP Solution File: SYN083+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN083+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 : n021.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 03:26:32 EDT 2023
% Result : Theorem 3.10s 1.20s
% Output : Proof 4.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN083+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n021.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 21:50:57 EDT 2023
% 0.13/0.35 % 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
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 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 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 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 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.75/0.92 Prover 4: Preprocessing ...
% 1.75/0.92 Prover 1: Preprocessing ...
% 2.02/0.97 Prover 3: Preprocessing ...
% 2.02/0.97 Prover 2: Preprocessing ...
% 2.02/0.97 Prover 6: Preprocessing ...
% 2.02/0.97 Prover 0: Preprocessing ...
% 2.02/0.97 Prover 5: Preprocessing ...
% 2.02/1.04 Prover 1: Constructing countermodel ...
% 2.02/1.04 Prover 4: Constructing countermodel ...
% 2.02/1.04 Prover 3: Constructing countermodel ...
% 2.02/1.05 Prover 6: Constructing countermodel ...
% 2.58/1.06 Prover 0: Proving ...
% 2.58/1.06 Prover 5: Proving ...
% 2.58/1.08 Prover 2: Proving ...
% 3.10/1.20 Prover 3: proved (566ms)
% 3.10/1.20
% 3.10/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.10/1.20
% 3.10/1.20 Prover 0: proved (579ms)
% 3.10/1.20
% 3.10/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.10/1.20
% 3.10/1.20 Prover 5: stopped
% 3.10/1.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.10/1.20 Prover 2: stopped
% 3.10/1.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.10/1.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.62/1.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.62/1.21 Prover 6: stopped
% 3.62/1.22 Prover 7: Preprocessing ...
% 3.62/1.22 Prover 8: Preprocessing ...
% 3.62/1.22 Prover 10: Preprocessing ...
% 3.62/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.62/1.22 Prover 11: Preprocessing ...
% 3.62/1.23 Prover 13: Preprocessing ...
% 3.62/1.25 Prover 8: Warning: ignoring some quantifiers
% 3.62/1.25 Prover 8: Constructing countermodel ...
% 3.62/1.26 Prover 10: Constructing countermodel ...
% 3.62/1.26 Prover 7: Constructing countermodel ...
% 4.01/1.27 Prover 11: Constructing countermodel ...
% 4.01/1.28 Prover 13: Warning: ignoring some quantifiers
% 4.01/1.28 Prover 13: Constructing countermodel ...
% 4.01/1.28 Prover 4: Found proof (size 16)
% 4.01/1.29 Prover 4: proved (654ms)
% 4.01/1.29 Prover 7: stopped
% 4.01/1.29 Prover 11: stopped
% 4.01/1.29 Prover 10: stopped
% 4.01/1.29 Prover 1: Found proof (size 16)
% 4.01/1.29 Prover 1: proved (659ms)
% 4.01/1.29 Prover 13: stopped
% 4.01/1.29 Prover 8: stopped
% 4.01/1.29
% 4.01/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.01/1.29
% 4.01/1.29 % SZS output start Proof for theBenchmark
% 4.01/1.29 Assumptions after simplification:
% 4.01/1.29 ---------------------------------
% 4.01/1.29
% 4.01/1.29 (p61_1)
% 4.01/1.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 4.01/1.33 (f(v3, v2) = v4) | ~ (f(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 4.01/1.33 ? [v5: $i] : (f(v1, v2) = v5 & f(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0:
% 4.01/1.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (f(v1, v2)
% 4.01/1.33 = v3) | ~ (f(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 4.01/1.33 $i] : (f(v5, v2) = v4 & f(v0, v1) = v5 & $i(v5) & $i(v4)))
% 4.01/1.33
% 4.01/1.33 (pel61)
% 4.01/1.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 4.01/1.34 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v6)
% 4.01/1.34 & f(v8, v3) = v9 & f(v7, v2) = v8 & f(v2, v3) = v4 & f(v1, v4) = v5 & f(v0,
% 4.01/1.34 v5) = v6 & f(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 4.01/1.34 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 4.01/1.34
% 4.01/1.34 (function-axioms)
% 4.01/1.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (f(v3,
% 4.01/1.34 v2) = v1) | ~ (f(v3, v2) = v0))
% 4.01/1.34
% 4.01/1.34 Those formulas are unsatisfiable:
% 4.01/1.34 ---------------------------------
% 4.01/1.34
% 4.01/1.34 Begin of proof
% 4.01/1.34 |
% 4.01/1.34 | ALPHA: (p61_1) implies:
% 4.01/1.34 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 4.01/1.34 | ~ (f(v1, v2) = v3) | ~ (f(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 4.01/1.34 | $i(v0) | ? [v5: $i] : (f(v5, v2) = v4 & f(v0, v1) = v5 & $i(v5) &
% 4.01/1.34 | $i(v4)))
% 4.01/1.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 4.01/1.35 | ~ (f(v3, v2) = v4) | ~ (f(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 4.01/1.35 | $i(v0) | ? [v5: $i] : (f(v1, v2) = v5 & f(v0, v5) = v4 & $i(v5) &
% 4.01/1.35 | $i(v4)))
% 4.01/1.35 |
% 4.01/1.35 | DELTA: instantiating (pel61) with fresh symbols all_4_0, all_4_1, all_4_2,
% 4.01/1.35 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9 gives:
% 4.01/1.35 | (3) ~ (all_4_0 = all_4_3) & f(all_4_1, all_4_6) = all_4_0 & f(all_4_2,
% 4.01/1.35 | all_4_7) = all_4_1 & f(all_4_7, all_4_6) = all_4_5 & f(all_4_8,
% 4.01/1.35 | all_4_5) = all_4_4 & f(all_4_9, all_4_4) = all_4_3 & f(all_4_9,
% 4.01/1.35 | all_4_8) = all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) &
% 4.01/1.35 | $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & $i(all_4_7) &
% 4.01/1.35 | $i(all_4_8) & $i(all_4_9)
% 4.01/1.35 |
% 4.01/1.35 | ALPHA: (3) implies:
% 4.01/1.35 | (4) ~ (all_4_0 = all_4_3)
% 4.01/1.35 | (5) $i(all_4_9)
% 4.01/1.35 | (6) $i(all_4_8)
% 4.01/1.35 | (7) $i(all_4_7)
% 4.01/1.35 | (8) $i(all_4_6)
% 4.01/1.35 | (9) $i(all_4_5)
% 4.01/1.35 | (10) $i(all_4_2)
% 4.01/1.35 | (11) f(all_4_9, all_4_8) = all_4_2
% 4.01/1.35 | (12) f(all_4_9, all_4_4) = all_4_3
% 4.01/1.35 | (13) f(all_4_8, all_4_5) = all_4_4
% 4.40/1.35 | (14) f(all_4_7, all_4_6) = all_4_5
% 4.40/1.35 | (15) f(all_4_2, all_4_7) = all_4_1
% 4.40/1.35 | (16) f(all_4_1, all_4_6) = all_4_0
% 4.40/1.36 |
% 4.40/1.36 | GROUND_INST: instantiating (1) with all_4_9, all_4_8, all_4_5, all_4_4,
% 4.40/1.36 | all_4_3, simplifying with (5), (6), (9), (12), (13) gives:
% 4.40/1.36 | (17) ? [v0: $i] : (f(v0, all_4_5) = all_4_3 & f(all_4_9, all_4_8) = v0 &
% 4.40/1.36 | $i(v0) & $i(all_4_3))
% 4.40/1.36 |
% 4.40/1.36 | GROUND_INST: instantiating (2) with all_4_2, all_4_7, all_4_6, all_4_1,
% 4.40/1.36 | all_4_0, simplifying with (7), (8), (10), (15), (16) gives:
% 4.40/1.36 | (18) ? [v0: $i] : (f(all_4_2, v0) = all_4_0 & f(all_4_7, all_4_6) = v0 &
% 4.40/1.36 | $i(v0) & $i(all_4_0))
% 4.40/1.36 |
% 4.40/1.36 | DELTA: instantiating (18) with fresh symbol all_11_0 gives:
% 4.40/1.36 | (19) f(all_4_2, all_11_0) = all_4_0 & f(all_4_7, all_4_6) = all_11_0 &
% 4.40/1.36 | $i(all_11_0) & $i(all_4_0)
% 4.40/1.36 |
% 4.40/1.36 | ALPHA: (19) implies:
% 4.40/1.36 | (20) f(all_4_7, all_4_6) = all_11_0
% 4.40/1.36 | (21) f(all_4_2, all_11_0) = all_4_0
% 4.40/1.36 |
% 4.40/1.36 | DELTA: instantiating (17) with fresh symbol all_15_0 gives:
% 4.40/1.36 | (22) f(all_15_0, all_4_5) = all_4_3 & f(all_4_9, all_4_8) = all_15_0 &
% 4.40/1.36 | $i(all_15_0) & $i(all_4_3)
% 4.40/1.36 |
% 4.40/1.36 | ALPHA: (22) implies:
% 4.40/1.36 | (23) f(all_4_9, all_4_8) = all_15_0
% 4.40/1.36 | (24) f(all_15_0, all_4_5) = all_4_3
% 4.40/1.36 |
% 4.40/1.36 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_15_0, all_4_8,
% 4.40/1.36 | all_4_9, simplifying with (11), (23) gives:
% 4.40/1.36 | (25) all_15_0 = all_4_2
% 4.40/1.36 |
% 4.40/1.36 | GROUND_INST: instantiating (function-axioms) with all_4_5, all_11_0, all_4_6,
% 4.40/1.37 | all_4_7, simplifying with (14), (20) gives:
% 4.40/1.37 | (26) all_11_0 = all_4_5
% 4.40/1.37 |
% 4.40/1.37 | REDUCE: (24), (25) imply:
% 4.40/1.37 | (27) f(all_4_2, all_4_5) = all_4_3
% 4.40/1.37 |
% 4.40/1.37 | REDUCE: (21), (26) imply:
% 4.40/1.37 | (28) f(all_4_2, all_4_5) = all_4_0
% 4.40/1.37 |
% 4.40/1.37 | GROUND_INST: instantiating (function-axioms) with all_4_3, all_4_0, all_4_5,
% 4.40/1.37 | all_4_2, simplifying with (27), (28) gives:
% 4.40/1.37 | (29) all_4_0 = all_4_3
% 4.40/1.37 |
% 4.40/1.37 | REDUCE: (4), (29) imply:
% 4.40/1.37 | (30) $false
% 4.40/1.37 |
% 4.40/1.37 | CLOSE: (30) is inconsistent.
% 4.40/1.37 |
% 4.40/1.37 End of proof
% 4.40/1.37 % SZS output end Proof for theBenchmark
% 4.40/1.37
% 4.40/1.37 767ms
%------------------------------------------------------------------------------