TSTP Solution File: SEU123+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU123+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 17:42:36 EDT 2023
% Result : Theorem 6.58s 1.66s
% Output : Proof 7.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU123+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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 : Wed Aug 23 18:02:20 EDT 2023
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 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 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 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 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
% 2.41/1.06 Prover 4: Preprocessing ...
% 2.41/1.06 Prover 1: Preprocessing ...
% 2.60/1.10 Prover 6: Preprocessing ...
% 2.60/1.10 Prover 2: Preprocessing ...
% 2.60/1.10 Prover 0: Preprocessing ...
% 2.60/1.10 Prover 3: Preprocessing ...
% 2.60/1.10 Prover 5: Preprocessing ...
% 5.21/1.47 Prover 2: Proving ...
% 5.21/1.47 Prover 1: Warning: ignoring some quantifiers
% 5.21/1.48 Prover 5: Proving ...
% 5.21/1.49 Prover 6: Proving ...
% 5.21/1.50 Prover 1: Constructing countermodel ...
% 5.21/1.50 Prover 3: Warning: ignoring some quantifiers
% 5.61/1.52 Prover 3: Constructing countermodel ...
% 5.61/1.52 Prover 4: Warning: ignoring some quantifiers
% 5.92/1.56 Prover 4: Constructing countermodel ...
% 5.92/1.61 Prover 0: Proving ...
% 6.58/1.66 Prover 6: proved (1025ms)
% 6.58/1.66
% 6.58/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.58/1.66
% 6.58/1.66 Prover 3: proved (1015ms)
% 6.58/1.66
% 6.58/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.58/1.66
% 6.58/1.66 Prover 0: stopped
% 6.58/1.66 Prover 5: stopped
% 6.58/1.66 Prover 2: stopped
% 6.58/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.58/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.58/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.58/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.58/1.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.90/1.69 Prover 1: Found proof (size 14)
% 6.90/1.69 Prover 1: proved (1067ms)
% 6.90/1.70 Prover 4: stopped
% 6.90/1.70 Prover 13: Preprocessing ...
% 6.90/1.71 Prover 11: Preprocessing ...
% 6.90/1.71 Prover 7: Preprocessing ...
% 6.90/1.72 Prover 10: Preprocessing ...
% 6.90/1.72 Prover 8: Preprocessing ...
% 6.90/1.73 Prover 7: stopped
% 6.90/1.73 Prover 13: stopped
% 6.90/1.73 Prover 10: stopped
% 7.35/1.75 Prover 11: stopped
% 7.63/1.83 Prover 8: Warning: ignoring some quantifiers
% 7.63/1.84 Prover 8: Constructing countermodel ...
% 7.63/1.85 Prover 8: stopped
% 7.63/1.85
% 7.63/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.63/1.85
% 7.63/1.85 % SZS output start Proof for theBenchmark
% 7.86/1.85 Assumptions after simplification:
% 7.86/1.85 ---------------------------------
% 7.86/1.85
% 7.86/1.85 (d10_xboole_0)
% 7.86/1.88 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) |
% 7.86/1.88 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i]
% 7.86/1.88 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 7.86/1.88
% 7.86/1.88 (t2_xboole_1)
% 7.86/1.88 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set,
% 7.86/1.88 v0) = v1) | ~ $i(v0))
% 7.86/1.88
% 7.86/1.88 (t3_xboole_1)
% 7.86/1.88 $i(empty_set) & ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0
% 7.86/1.89 & $i(v0))
% 7.86/1.89
% 7.86/1.89 Further assumptions not needed in the proof:
% 7.86/1.89 --------------------------------------------
% 7.86/1.89 antisymmetry_r2_hidden, commutativity_k3_xboole_0, d1_xboole_0, d3_tarski,
% 7.86/1.89 d3_xboole_0, d7_xboole_0, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 7.86/1.89 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 7.86/1.89 symmetry_r1_xboole_0, t1_xboole_1, t3_xboole_0, t4_xboole_0, t6_boole, t7_boole,
% 7.86/1.89 t8_boole
% 7.86/1.89
% 7.86/1.89 Those formulas are unsatisfiable:
% 7.86/1.89 ---------------------------------
% 7.86/1.89
% 7.86/1.89 Begin of proof
% 7.86/1.89 |
% 7.86/1.89 | ALPHA: (d10_xboole_0) implies:
% 7.86/1.89 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~
% 7.86/1.89 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) =
% 7.86/1.89 | v2))
% 7.86/1.89 |
% 7.86/1.89 | ALPHA: (t2_xboole_1) implies:
% 7.86/1.89 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)
% 7.86/1.89 | | ~ $i(v0))
% 7.86/1.89 |
% 7.86/1.89 | ALPHA: (t3_xboole_1) implies:
% 7.86/1.89 | (3) $i(empty_set)
% 7.86/1.89 | (4) ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, empty_set) = 0 &
% 7.86/1.89 | $i(v0))
% 7.86/1.89 |
% 7.86/1.89 | DELTA: instantiating (4) with fresh symbol all_21_0 gives:
% 7.86/1.89 | (5) ~ (all_21_0 = empty_set) & subset(all_21_0, empty_set) = 0 &
% 7.86/1.89 | $i(all_21_0)
% 7.86/1.89 |
% 7.86/1.89 | ALPHA: (5) implies:
% 7.86/1.89 | (6) ~ (all_21_0 = empty_set)
% 7.86/1.89 | (7) $i(all_21_0)
% 7.86/1.89 | (8) subset(all_21_0, empty_set) = 0
% 7.86/1.89 |
% 7.86/1.90 | GROUND_INST: instantiating (1) with all_21_0, empty_set, simplifying with (3),
% 7.86/1.90 | (7), (8) gives:
% 7.86/1.90 | (9) all_21_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set,
% 7.86/1.90 | all_21_0) = v0)
% 7.86/1.90 |
% 7.86/1.90 | BETA: splitting (9) gives:
% 7.86/1.90 |
% 7.86/1.90 | Case 1:
% 7.86/1.90 | |
% 7.86/1.90 | | (10) all_21_0 = empty_set
% 7.86/1.90 | |
% 7.86/1.90 | | REDUCE: (6), (10) imply:
% 7.86/1.90 | | (11) $false
% 7.86/1.90 | |
% 7.86/1.90 | | CLOSE: (11) is inconsistent.
% 7.86/1.90 | |
% 7.86/1.90 | Case 2:
% 7.86/1.90 | |
% 7.86/1.90 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, all_21_0) = v0)
% 7.86/1.90 | |
% 7.86/1.90 | | DELTA: instantiating (12) with fresh symbol all_43_0 gives:
% 7.86/1.90 | | (13) ~ (all_43_0 = 0) & subset(empty_set, all_21_0) = all_43_0
% 7.86/1.90 | |
% 7.86/1.90 | | ALPHA: (13) implies:
% 7.86/1.90 | | (14) ~ (all_43_0 = 0)
% 7.86/1.90 | | (15) subset(empty_set, all_21_0) = all_43_0
% 7.86/1.90 | |
% 7.86/1.90 | | GROUND_INST: instantiating (2) with all_21_0, all_43_0, simplifying with
% 7.86/1.90 | | (7), (15) gives:
% 7.86/1.90 | | (16) all_43_0 = 0
% 7.86/1.90 | |
% 7.86/1.90 | | REDUCE: (14), (16) imply:
% 7.86/1.90 | | (17) $false
% 7.86/1.90 | |
% 7.86/1.90 | | CLOSE: (17) is inconsistent.
% 7.86/1.90 | |
% 7.86/1.90 | End of split
% 7.86/1.90 |
% 7.86/1.90 End of proof
% 7.86/1.90 % SZS output end Proof for theBenchmark
% 7.86/1.90
% 7.86/1.90 1296ms
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