TSTP Solution File: SET875+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET875+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Thu Aug 31 15:26:52 EDT 2023
% Result : Theorem 4.18s 1.32s
% Output : Proof 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET875+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % 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 14:33:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.62/0.62 ________ _____
% 0.62/0.62 ___ __ \_________(_)________________________________
% 0.62/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.62
% 0.62/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.62 (2023-06-19)
% 0.62/0.62
% 0.62/0.62 (c) Philipp Rümmer, 2009-2023
% 0.62/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.62 Amanda Stjerna.
% 0.62/0.62 Free software under BSD-3-Clause.
% 0.62/0.62
% 0.62/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.62
% 0.62/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.63 Running up to 7 provers in parallel.
% 0.73/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.73/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.73/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.73/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.73/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.73/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.73/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.82/0.99 Prover 4: Preprocessing ...
% 1.82/0.99 Prover 1: Preprocessing ...
% 2.26/1.04 Prover 6: Preprocessing ...
% 2.26/1.04 Prover 2: Preprocessing ...
% 2.26/1.04 Prover 3: Preprocessing ...
% 2.26/1.04 Prover 0: Preprocessing ...
% 2.26/1.04 Prover 5: Preprocessing ...
% 3.24/1.19 Prover 3: Warning: ignoring some quantifiers
% 3.43/1.19 Prover 1: Warning: ignoring some quantifiers
% 3.43/1.20 Prover 5: Proving ...
% 3.43/1.20 Prover 6: Proving ...
% 3.43/1.20 Prover 3: Constructing countermodel ...
% 3.43/1.20 Prover 4: Warning: ignoring some quantifiers
% 3.43/1.20 Prover 1: Constructing countermodel ...
% 3.43/1.21 Prover 0: Proving ...
% 3.43/1.21 Prover 2: Proving ...
% 3.43/1.21 Prover 4: Constructing countermodel ...
% 4.18/1.32 Prover 3: proved (682ms)
% 4.18/1.32
% 4.18/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.32
% 4.18/1.32 Prover 5: stopped
% 4.18/1.33 Prover 6: proved (683ms)
% 4.18/1.33
% 4.18/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.33
% 4.18/1.33 Prover 0: stopped
% 4.18/1.34 Prover 2: proved (688ms)
% 4.18/1.34
% 4.18/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.34
% 4.18/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.18/1.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.18/1.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.18/1.34 Prover 1: Found proof (size 11)
% 4.18/1.34 Prover 1: proved (699ms)
% 4.18/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.18/1.34 Prover 4: stopped
% 4.18/1.34 Prover 10: Preprocessing ...
% 4.18/1.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.18/1.34 Prover 7: Preprocessing ...
% 4.18/1.34 Prover 8: Preprocessing ...
% 4.18/1.35 Prover 13: Preprocessing ...
% 4.18/1.35 Prover 11: Preprocessing ...
% 4.64/1.37 Prover 13: stopped
% 4.64/1.37 Prover 11: stopped
% 4.64/1.38 Prover 7: Warning: ignoring some quantifiers
% 4.64/1.39 Prover 7: Constructing countermodel ...
% 4.64/1.39 Prover 8: Warning: ignoring some quantifiers
% 4.64/1.39 Prover 7: stopped
% 4.64/1.39 Prover 10: Warning: ignoring some quantifiers
% 4.64/1.40 Prover 8: Constructing countermodel ...
% 4.64/1.40 Prover 10: Constructing countermodel ...
% 4.64/1.40 Prover 10: stopped
% 4.64/1.40 Prover 8: stopped
% 4.64/1.40
% 4.64/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.64/1.40
% 4.64/1.40 % SZS output start Proof for theBenchmark
% 4.64/1.40 Assumptions after simplification:
% 4.64/1.40 ---------------------------------
% 4.64/1.41
% 4.64/1.41 (d1_tarski)
% 4.64/1.44 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) |
% 4.64/1.44 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 &
% 4.64/1.44 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i]
% 4.64/1.44 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2:
% 4.64/1.44 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 =
% 4.64/1.44 0 | ~ (in(v0, v1) = v2))))
% 4.64/1.44
% 4.64/1.44 (l25_zfmisc_1)
% 4.64/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (disjoint(v2, v1) = 0) | ~
% 4.64/1.44 (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 4.64/1.44 in(v0, v1) = v3))
% 4.64/1.44
% 4.64/1.44 (t16_zfmisc_1)
% 4.64/1.44 ? [v0: $i] : ? [v1: $i] : (disjoint(v1, v1) = 0 & singleton(v0) = v1 &
% 4.64/1.44 $i(v1) & $i(v0))
% 4.64/1.44
% 4.64/1.44 Further assumptions not needed in the proof:
% 4.64/1.44 --------------------------------------------
% 4.64/1.44 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0
% 4.64/1.44
% 4.64/1.44 Those formulas are unsatisfiable:
% 4.64/1.44 ---------------------------------
% 4.64/1.44
% 4.64/1.44 Begin of proof
% 4.64/1.44 |
% 4.64/1.44 | ALPHA: (d1_tarski) implies:
% 4.64/1.44 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 4.64/1.44 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) &
% 4.64/1.44 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2))))
% 4.64/1.44 |
% 4.64/1.45 | DELTA: instantiating (t16_zfmisc_1) with fresh symbols all_11_0, all_11_1
% 4.64/1.45 | gives:
% 4.64/1.45 | (2) disjoint(all_11_0, all_11_0) = 0 & singleton(all_11_1) = all_11_0 &
% 4.64/1.45 | $i(all_11_0) & $i(all_11_1)
% 4.64/1.45 |
% 4.64/1.45 | ALPHA: (2) implies:
% 4.64/1.45 | (3) $i(all_11_1)
% 4.64/1.45 | (4) $i(all_11_0)
% 4.64/1.45 | (5) singleton(all_11_1) = all_11_0
% 4.64/1.45 | (6) disjoint(all_11_0, all_11_0) = 0
% 4.64/1.45 |
% 4.64/1.45 | GROUND_INST: instantiating (1) with all_11_1, all_11_0, simplifying with (3),
% 4.64/1.45 | (4), (5) gives:
% 4.64/1.45 | (7) ! [v0: any] : (v0 = all_11_1 | ~ (in(v0, all_11_0) = 0) | ~ $i(v0))
% 4.64/1.45 | & ! [v0: int] : (v0 = 0 | ~ (in(all_11_1, all_11_0) = v0))
% 4.64/1.45 |
% 4.64/1.45 | ALPHA: (7) implies:
% 4.64/1.45 | (8) ! [v0: int] : (v0 = 0 | ~ (in(all_11_1, all_11_0) = v0))
% 4.64/1.45 |
% 4.64/1.45 | GROUND_INST: instantiating (l25_zfmisc_1) with all_11_1, all_11_0, all_11_0,
% 4.64/1.45 | simplifying with (3), (4), (5), (6) gives:
% 4.64/1.45 | (9) ? [v0: int] : ( ~ (v0 = 0) & in(all_11_1, all_11_0) = v0)
% 4.64/1.45 |
% 4.64/1.45 | DELTA: instantiating (9) with fresh symbol all_21_0 gives:
% 4.64/1.45 | (10) ~ (all_21_0 = 0) & in(all_11_1, all_11_0) = all_21_0
% 4.64/1.45 |
% 4.64/1.45 | ALPHA: (10) implies:
% 4.64/1.45 | (11) ~ (all_21_0 = 0)
% 4.64/1.45 | (12) in(all_11_1, all_11_0) = all_21_0
% 4.64/1.45 |
% 4.64/1.45 | GROUND_INST: instantiating (8) with all_21_0, simplifying with (12) gives:
% 4.64/1.45 | (13) all_21_0 = 0
% 4.64/1.45 |
% 4.64/1.45 | REDUCE: (11), (13) imply:
% 4.64/1.45 | (14) $false
% 5.16/1.46 |
% 5.16/1.46 | CLOSE: (14) is inconsistent.
% 5.16/1.46 |
% 5.16/1.46 End of proof
% 5.16/1.46 % SZS output end Proof for theBenchmark
% 5.16/1.46
% 5.16/1.46 839ms
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